The optimal solutions are listed as follows:

numOfHGT=5    numOfDuplications=2    numOfLoss=2
((((((1,2),(1,2))^,1)^,4),(2*,5)*),(((1*,4)*,5),3*));

numOfHGT=4    numOfDuplications=2    numOfLoss=3
((((((1,2),(1,2))^,1)^,4)*,(2*,5)),(((1*,4),5*),3));

numOfHGT=5    numOfDuplications=2    numOfLoss=2
((((((1,2),(1,2))^,1)^*,4)*,(2*,5)),(((1*,4),5*),3));

numOfHGT=5    numOfDuplications=2    numOfLoss=2
((((((1,2),(1,2))^,1)^,4*)*,(2*,5)),(((1*,4),5*),3));

numOfHGT=6    numOfDuplications=2    numOfLoss=1
((((((1,2),(1,2))^,1)^,4*),(2*,5)*),(((1*,4)*,5)*,3));

numOfHGT=6    numOfDuplications=2    numOfLoss=1
((((((1,2),(1,2))^,1)^,4*),(2*,5)*),(((1*,4),5*)*,3));

numOfHGT=5    numOfDuplications=2    numOfLoss=2
((((((1,2),(1,2))^,1)^,4),(2*,5)*),(((1,4*)*,5),3*));

numOfHGT=5    numOfDuplications=2    numOfLoss=2
((((((1,2),(1,2))^,1)^*,4),(2*,5)*),(((1,4*),5*),3));

numOfHGT=6    numOfDuplications=2    numOfLoss=1
((((((1,2),(1,2))^,1)^,4*),(2*,5)*),(((1,4*)*,5)*,3));

numOfHGT=6    numOfDuplications=2    numOfLoss=1
((((((1,2),(1,2))^,1)^,4*),(2*,5)*),(((1,4*),5*)*,3));

numOfHGT=6    numOfDuplications=2    numOfLoss=1
((((((1,2),(1,2))^,1)^*,4)*,(2,5*)),(((1,4*),5*),3*));

numOfHGT=5    numOfDuplications=2    numOfLoss=2
((((((1,2),(1,2))^,1)^*,4),(2,5*)*),(((1,4*),5*),3));

numOfHGT=7    numOfDuplications=1    numOfLoss=1
((((((1*,2),(1*,2))^,1),4),(2*,5)*),(((1*,4)*,5),3*));

numOfHGT=6    numOfDuplications=1    numOfLoss=2
((((((1*,2),(1*,2))^,1),4)*,(2*,5)),(((1*,4),5*),3));

numOfHGT=7    numOfDuplications=1    numOfLoss=1
((((((1*,2),(1*,2))^,1)*,4)*,(2*,5)),(((1*,4),5*),3));

numOfHGT=7    numOfDuplications=1    numOfLoss=1
((((((1*,2),(1*,2))^,1),4*)*,(2*,5)),(((1*,4),5*),3));

numOfHGT=8    numOfDuplications=1    numOfLoss=0
((((((1*,2),(1*,2))^,1),4*),(2*,5)*),(((1*,4)*,5)*,3));

numOfHGT=8    numOfDuplications=1    numOfLoss=0
((((((1*,2),(1*,2))^,1),4*),(2*,5)*),(((1*,4),5*)*,3));

numOfHGT=8    numOfDuplications=1    numOfLoss=0
((((((1*,2),(1*,2))^*,1),4*),(2,5*)),(((1*,4)*,5)*,3));

numOfHGT=8    numOfDuplications=1    numOfLoss=0
((((((1*,2),(1*,2))^*,1),4*),(2,5*)),(((1*,4),5*)*,3));

numOfHGT=7    numOfDuplications=1    numOfLoss=1
((((((1*,2),(1*,2))^,1),4),(2*,5)*),(((1,4*)*,5),3*));

numOfHGT=7    numOfDuplications=1    numOfLoss=1
((((((1*,2),(1*,2))^,1)*,4),(2*,5)*),(((1,4*),5*),3));

numOfHGT=8    numOfDuplications=1    numOfLoss=0
((((((1*,2),(1*,2))^,1),4*),(2*,5)*),(((1,4*)*,5)*,3));

numOfHGT=8    numOfDuplications=1    numOfLoss=0
((((((1*,2),(1*,2))^,1),4*),(2*,5)*),(((1,4*),5*)*,3));

numOfHGT=8    numOfDuplications=1    numOfLoss=0
((((((1*,2),(1*,2))^,1)*,4)*,(2,5*)),(((1,4*),5*),3*));

numOfHGT=7    numOfDuplications=1    numOfLoss=1
((((((1*,2),(1*,2))^,1)*,4),(2,5*)*),(((1,4*),5*),3));

numOfHGT=8    numOfDuplications=1    numOfLoss=0
((((((1*,2),(1*,2))^*,1),4*),(2,5*)),(((1,4*)*,5)*,3));

numOfHGT=8    numOfDuplications=1    numOfLoss=0
((((((1*,2),(1*,2))^*,1),4*),(2,5*)),(((1,4*),5*)*,3));

numOfHGT=8    numOfDuplications=1    numOfLoss=0
((((((1*,2)*,(1,2*)),1)^,4*),(2,5*)),(((1*,4)*,5)*,3));

numOfHGT=8    numOfDuplications=1    numOfLoss=0
((((((1*,2)*,(1,2*)),1)^,4*),(2,5*)),(((1*,4),5*)*,3));

numOfHGT=8    numOfDuplications=1    numOfLoss=0
((((((1*,2)*,(1,2*)),1)^,4*),(2,5*)),(((1,4*)*,5)*,3));

numOfHGT=8    numOfDuplications=1    numOfLoss=0
((((((1*,2)*,(1,2*)),1)^,4*),(2,5*)),(((1,4*),5*)*,3));

numOfHGT=8    numOfDuplications=0    numOfLoss=1
((((((1*,2),(1,2*)*),1),4),(2*,5)*),(((1*,4)*,5),3*));

numOfHGT=7    numOfDuplications=0    numOfLoss=2
((((((1*,2),(1,2*)*),1),4)*,(2*,5)),(((1*,4),5*),3));

numOfHGT=8    numOfDuplications=0    numOfLoss=1
((((((1*,2),(1,2*)*),1)*,4)*,(2*,5)),(((1*,4),5*),3));

numOfHGT=8    numOfDuplications=0    numOfLoss=1
((((((1*,2),(1,2*)*),1),4*)*,(2*,5)),(((1*,4),5*),3));

numOfHGT=9    numOfDuplications=0    numOfLoss=0
((((((1*,2),(1,2*)*),1),4*),(2*,5)*),(((1*,4)*,5)*,3));

numOfHGT=9    numOfDuplications=0    numOfLoss=0
((((((1*,2),(1,2*)*),1),4*),(2*,5)*),(((1*,4),5*)*,3));

numOfHGT=9    numOfDuplications=0    numOfLoss=0
((((((1*,2),(1,2*)*)*,1),4*),(2,5*)),(((1*,4)*,5)*,3));

numOfHGT=9    numOfDuplications=0    numOfLoss=0
((((((1*,2),(1,2*)*)*,1),4*),(2,5*)),(((1*,4),5*)*,3));

numOfHGT=8    numOfDuplications=0    numOfLoss=1
((((((1*,2),(1,2*)*),1),4),(2*,5)*),(((1,4*)*,5),3*));

numOfHGT=8    numOfDuplications=0    numOfLoss=1
((((((1*,2),(1,2*)*),1)*,4),(2*,5)*),(((1,4*),5*),3));

numOfHGT=9    numOfDuplications=0    numOfLoss=0
((((((1*,2),(1,2*)*),1),4*),(2*,5)*),(((1,4*)*,5)*,3));

numOfHGT=9    numOfDuplications=0    numOfLoss=0
((((((1*,2),(1,2*)*),1),4*),(2*,5)*),(((1,4*),5*)*,3));

numOfHGT=9    numOfDuplications=0    numOfLoss=0
((((((1*,2),(1,2*)*),1)*,4)*,(2,5*)),(((1,4*),5*),3*));

numOfHGT=8    numOfDuplications=0    numOfLoss=1
((((((1*,2),(1,2*)*),1)*,4),(2,5*)*),(((1,4*),5*),3));

numOfHGT=9    numOfDuplications=0    numOfLoss=0
((((((1*,2),(1,2*)*)*,1),4*),(2,5*)),(((1,4*)*,5)*,3));

numOfHGT=9    numOfDuplications=0    numOfLoss=0
((((((1*,2),(1,2*)*)*,1),4*),(2,5*)),(((1,4*),5*)*,3));

numOfHGT=8    numOfDuplications=0    numOfLoss=1
((((((1,2*)*,(1*,2)),1),4),(2*,5)*),(((1*,4)*,5),3*));

numOfHGT=7    numOfDuplications=0    numOfLoss=2
((((((1,2*)*,(1*,2)),1),4)*,(2*,5)),(((1*,4),5*),3));

numOfHGT=8    numOfDuplications=0    numOfLoss=1
((((((1,2*)*,(1*,2)),1)*,4)*,(2*,5)),(((1*,4),5*),3));

numOfHGT=8    numOfDuplications=0    numOfLoss=1
((((((1,2*)*,(1*,2)),1),4*)*,(2*,5)),(((1*,4),5*),3));

numOfHGT=9    numOfDuplications=0    numOfLoss=0
((((((1,2*)*,(1*,2)),1),4*),(2*,5)*),(((1*,4)*,5)*,3));

numOfHGT=9    numOfDuplications=0    numOfLoss=0
((((((1,2*)*,(1*,2)),1),4*),(2*,5)*),(((1*,4),5*)*,3));

numOfHGT=9    numOfDuplications=0    numOfLoss=0
((((((1,2*)*,(1*,2))*,1),4*),(2,5*)),(((1*,4)*,5)*,3));

numOfHGT=9    numOfDuplications=0    numOfLoss=0
((((((1,2*)*,(1*,2))*,1),4*),(2,5*)),(((1*,4),5*)*,3));

numOfHGT=8    numOfDuplications=0    numOfLoss=1
((((((1,2*)*,(1*,2)),1),4),(2*,5)*),(((1,4*)*,5),3*));

numOfHGT=8    numOfDuplications=0    numOfLoss=1
((((((1,2*)*,(1*,2)),1)*,4),(2*,5)*),(((1,4*),5*),3));

numOfHGT=9    numOfDuplications=0    numOfLoss=0
((((((1,2*)*,(1*,2)),1),4*),(2*,5)*),(((1,4*)*,5)*,3));

numOfHGT=9    numOfDuplications=0    numOfLoss=0
((((((1,2*)*,(1*,2)),1),4*),(2*,5)*),(((1,4*),5*)*,3));

numOfHGT=9    numOfDuplications=0    numOfLoss=0
((((((1,2*)*,(1*,2)),1)*,4)*,(2,5*)),(((1,4*),5*),3*));

numOfHGT=8    numOfDuplications=0    numOfLoss=1
((((((1,2*)*,(1*,2)),1)*,4),(2,5*)*),(((1,4*),5*),3));

numOfHGT=9    numOfDuplications=0    numOfLoss=0
((((((1,2*)*,(1*,2))*,1),4*),(2,5*)),(((1,4*)*,5)*,3));

numOfHGT=9    numOfDuplications=0    numOfLoss=0
((((((1,2*)*,(1*,2))*,1),4*),(2,5*)),(((1,4*),5*)*,3));

numOfHGT=8    numOfDuplications=1    numOfLoss=0
((((((1,2*),(1*,2)*),1)^,4*),(2,5*)),(((1*,4)*,5)*,3));

numOfHGT=8    numOfDuplications=1    numOfLoss=0
((((((1,2*),(1*,2)*),1)^,4*),(2,5*)),(((1*,4),5*)*,3));

numOfHGT=8    numOfDuplications=1    numOfLoss=0
((((((1,2*),(1*,2)*),1)^,4*),(2,5*)),(((1,4*)*,5)*,3));

numOfHGT=8    numOfDuplications=1    numOfLoss=0
((((((1,2*),(1*,2)*),1)^,4*),(2,5*)),(((1,4*),5*)*,3));

numOfHGT=7    numOfDuplications=2    numOfLoss=0
((((((1,2*),(1,2*))^,1)^,4*),(2,5*)),(((1*,4)*,5)*,3));

numOfHGT=7    numOfDuplications=2    numOfLoss=0
((((((1,2*),(1,2*))^,1)^,4*),(2,5*)),(((1*,4),5*)*,3));

numOfHGT=7    numOfDuplications=2    numOfLoss=0
((((((1,2*),(1,2*))^,1)^,4*),(2,5*)),(((1,4*)*,5)*,3));

numOfHGT=7    numOfDuplications=2    numOfLoss=0
((((((1,2*),(1,2*))^,1)^,4*),(2,5*)),(((1,4*),5*)*,3));


Total Cost=9

Total number of solutions=72